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Proving that the matrix is invertible given the eigenvalues?

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Given an unknown matrix with eigenvalues 1,2,3, prove that it is invertible?

    3. The attempt at a solution
    If the det = 0, then there exists an eigenvalue = 0. Since none of the eigenvalues are 0, then the det ≠ 0 and thus the matrix is invertible. Is this a valid proof?
     
  2. jcsd
  3. Apr 16, 2012 #2

    HallsofIvy

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    Yes, it is.
     
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